Think you've got that backwards. A dish that's wider will have a narrower beamwidth along it's major axis and provided it's skewed properly for the satellite it's pointing at (and of course has a feedhorn to illuminate it's oval shape properly), will reject interference from adjacent satellites better. A taller dish would be the opposite and have a narrower beamwidth vertically, which probably wouldn't help with rejecting interference from adjacent satellites very much.
A dish that is wide can pickup more than one satellite.
Any dish can pickup more than one satellite, but at different focal points. A wider dsih moves the focal points of the incoming signals from the different satellites farther apart along it's major axis, thus making placement of the multiple feedhorns easier and more practicle. This also ties into how it rejects interference from adjacent satellites better as the focal points from the incoming signals of the adjacent satellites will be farther apart such that the feedhorns placed at those focal points will receive signal mostly from only the one satellite that has that focal point.
As for using a dish network or directv dish for FTA, the answer is it's too small. With a dish this small the focal points for satellites placed 2 degrees apart are so close together that any feedhorn placed at those focal points would actually be at the focal point of more than one satellite and thus would be receiving signals from those multiple satellites all at the same time. This is what causes interference from adjacent satellites and would make it very difficult (likely impossible) to receive most FTA signals. The reason it works for Dish and DTV is they use a portion of the Ku band (12.2 -12.7Ghz) that other satellites don't use and they are careful to space their satellites wider apart or if they do happen to have a couple of satellites close together they don't use overlapping frequencies and polarities on the transponders on those satellites. Also the fact they use these different frequencies means the LNB on their dishes is not going to get most FTA signals, but this is kinda moot since the dish is way too small anyway. Anyway, when you see someone with an 18" dish hooked up to a fta receiver they're generally involved in something not legal and aren't receiving FTA signals.